Solve (6+3/5+1/10)div51/2

$$( 6 + \frac { 3 } { 5 } + \frac { 1 } { 10 } ) \div 5 \frac { 1 } { 2 }$$

Evaluate

$$\frac{67}{55}\approx 1.218181818$$

Solution Steps

Convert 6 to fraction \frac{30}{5}.

$$\frac{\frac{30}{5}+\frac{3}{5}+\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Since \frac{30}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{30+3}{5}+\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Add 30 and 3 to get 33.

$$\frac{\frac{33}{5}+\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{33}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{66}{10}+\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Since \frac{66}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{66+1}{10}}{\frac{5\times 2+1}{2}}$$

Add 66 and 1 to get 67.

$$\frac{\frac{67}{10}}{\frac{5\times 2+1}{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{67}{10}}{\frac{10+1}{2}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{67}{10}}{\frac{11}{2}}$$

Divide \frac{67}{10} by \frac{11}{2} by multiplying \frac{67}{10} by the reciprocal of \frac{11}{2}.

$$\frac{67}{10}\times \frac{2}{11}$$

Multiply \frac{67}{10} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{67\times 2}{10\times 11}$$

Do the multiplications in the fraction \frac{67\times 2}{10\times 11}.

$$\frac{134}{110}$$

Reduce the fraction \frac{134}{110} to lowest terms by extracting and canceling out 2.

$$\frac{67}{55}$$

Factor

$$\frac{67}{5 \cdot 11} = 1\frac{12}{55} = 1.2181818181818183$$